To understand Cell Flow Cytometry, it is not ultimately necessary to understand how and why fluorescence works - however, I think it's quite a good opportunity to look at that topic too.
But don't worry, we won't get too deeply involved in the physics part.

All you should know is a quite simple principle.
Visible light (light of the visible spectrum) is an electromagentic wave.
If light hits an atom that is fluorescent, it can excite an electron of that atom, and move it to a state of higher energy. In this state, the whole atom is a little bit unstable, and you can imagine that this is not a very favourable situation for the atom, therefore the electron will sooner or later "drop" back on his original energy level, his original state of energy.
But as we all (hopefully? XD) know, energy cannot be simply "lost", so what happens with the energy that the electron took up when it was excited?
The electron itself will emit an electromagentic wave and thus produce light!
This is what fluorescence is all about.
However, it is worth noticing that the emitted light is always of lower energy than the light that excited the electron. Sounds logical, doesn't it? You can imagine some of the energy being used up for "moving" the electron from the lower state to the higher energy state. The remaining energy is released as light when it falls back.
Lower energy basically means a higher wavelength (imagine you slap a person, and everytime you slap is a "wave". The longer the time between the slaps, thus the longer the "wave", the less the person will be hurt. I always find hitting people to be a good method to remember things ;D ), and this also means that the light that is emitted will have a different "color" then the one that was absorbed.

So now that we know that I want to show you a very cool technique to count cells in a sample - and it's also very simple to understand!

So how does this method work?
On the picture to the rigth you can see something like a long and small capillary. Via a special technique, the cells are forced through this capillary individually, this means only one cell passes the capillary at a time.
At some point there is an optical window. This means that a laser beam hits the sample in the capillary!
In order to make the different cells distinguishable from each other, you have to prepare different fluorescent markers (fluorescent dyes), for example you have a red dye that binds to a cell of type "A" and a green dye that binds to cell "B". For the third cell type, let's call it "C", we don't need a dye. You will soon see why.

As soon as a cell of type A or B passes the optical window, the laser beam will excite the fluorescence dye molecule on that cell. The dye will emit light of a specific spectrum, which you can measure - by determining the wavelength (i.e. the color of the light) you can now easily distinguish between a cell A or a cell B!
So what if it were a cell of type C? Then you wouldn't get any emission signal, and again would now that the cell that has just passed the optical window is of Type C.

In a medical application your question could for example be: What is the ratio between B- and T-cells in my patient's blood? Both these cell types are part of the immune system and in a healthy human this ratio is a relatively fixed number. However, you probably can immediately think of a disease that affects the immune system, in particular human T-cells : an infection with the HIV virus.
The virus invades T-cells and destroys them from within, therefore compromising the immune system of the patient.
If you apply a drug therapy against the virus, you could use the Cell Flow Cytometry to monitor the number of T-cells, and you could see if the number would remain stable (meaning the drug works) or if the number drops.

So try to guess now, what else we could use that method for. Is it just counting and thus quantification of cells in a sample?
Of course not!
Consider the schematic picture on the rigth. The process that is illustrated there is called Fluorescence Activated Cell Sorting(FACS).
In this case, our fluorescent dyes need to have a charge. After passing the optical window, a scanner detects the color of the sample and consequently adjusts an electrical field through which the cell then passes. If the cell is, for example, green it shall be deflected to the left (see picture). In order to achieve this, a positive charge is applied to the drop that contains the cell as soon as it leaves the optical window. Cells with red dye will get a negative charge and be deflected to the right and cells with no charge will not be deflected at all. This deflection allows a separation of the different cell types, and you can collect the fractions below.
The effectiveness of this procedure is not exactly 100%, so you have to perform further sorting steps with the fractions, in order to achieve a higher purity of your sample

So, that's basically it ^^
If you've read through all of this... you probably understand now at least the principle of fluorescence and one type of application!
I don't know if you can understand my fascination for this topic and if it's even remotely interesting for you XD
Anyway, just let me know if this type of stuff is interesting to you, because I'd love to tell you more :3

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